Acoustic Impendences in this Ultrasound Imaging problem

[nao113]

Homework Statement

Problem:a)Plot amplitude of Echoes 3 and 4 as a variety of R = 0-1. Discuss reasonable range of R which is suitable for imaging.
b) R=|z1-z2|/(z1+z2) (acoustic impedances: z1 and z2). Calculate acoustic impedances of fat, water, and other materials composed of human body from multiplication of density by sound speed. Discuss the differences of reflection coefficients between the area 1, which contains water and the other area 2, which contains fat.
c)Discuss about real imaging, by considering the difference in problem b)

Relevant Equations

I put that below

Question:

Answer:
I don't understand about a and c. I just tried to solve b but my answer is still lacking for part b. Can anyone guide me about how to solve these problems and what I did wrong in part b.

 

[haruspex]

Homework Statement:: Problem:a)Plot amplitude of Echoes 3 and 4 as a variety of R = 0-1. Discuss reasonable range of R which is suitable for imaging.

I don't understand about a

It is asking you to plot graphs of $T^2R^3$ and $T^4R$ against R, over the range $0<R<1$, given that $T=1-R$.

For b, https://www.schoolphysics.co.uk/age16-19/Sound/text/Acoustic_impedance/index.html gives a slightly lower value for $z_{fat}$, making about a 14% difference to the answer. But you should work with whatever values you were given.
You have mistyped a sign in the denominator.

Btw, the word is "artefact", not "arch-fact".